1. Field of the Invention
The invention relates to a Fuzzy backward reasoning device useful for application fields requiring reasoning of a cause that causes a feature quantity such for example as target classification in air traffic control, including diagnoses in medical services and fault diagnosis in plants, etc.
2. Description of the Prior Art
Referring to FIG. 6, a prior art Fuzzy backward reasoning device is illustrated in a block diagram. The device is disclosed for example in "Method of Solution to Fuzzy Inverse Problem " Tsukamoto and Tashiro, Papers in the 3rd System Symposium supported by the Society of Instrument and Control Engineers, Vol. 15, No. 1, PP 21 to 25, 1979. As shown in the same figure, a Fuzzy backward reasoning device 5 includes batch reasoning device 51 for receiving all of feature quantities (b.sub.j ) and causal relations ( r.sup.j) for Fuzzy backward reasoning and outputting reasoned results (a.sub.i), and causality relation storage device 3 for outputting the causality relations ( r.sup.j) previously stored in the batch reasoning device 51.
Referring to FIG. 7, a situation of solving a problem in the Fuzzy backward reasoning is illustrated. Designated at 52 is a causality relation.
m causes a.sub.1, a.sub.2. . . , a.sub.m are inputted into the causality relation 52, which in turn outputs n feature quantities b.sub.1, b.sub.2, . . . , b.sub.n. a.sub.1, b.sub.j take values from 0 to 1 and indicate the possibility of each cause and the intensity of each feature quantity respectively. These quantities are expressed by row vectors EQU =(a.sub.1, a.sub.2. . . a.sub.m) (1) EQU b=(b.sub.1, b.sub.2. . . b.sub.n) (2)
The causality relation 52 is represented by a m.times.n matrix R=(r.sub.ij) with elements r.sub.ij taking a value of from 0 to 1, the element indicating a degree where the feature quantity b.sub.j is caused by the cause a.sub.i. If each column vector is designated by r.sup.j, then r.sup.j denotes a causality relation that causes the feature quantity b.sub.j. The matrix R is expressed by ##EQU1##
The relationship among , b, and R, illustrated in FIG. 7 satisfies EQU o R= b (4)
Here, the symbol 0 indicates max-min composition. That is, for each element ##EQU2## Here, V denotes max operation and min operation. The causality relation R is given as a knowledge and the feature quantity b is observable. Hereby, the cause that causes such a feature quantity b can be reasoned. The reasoning is given by the Fuzzy backward reasoning. A result of the reasoning gives EQU a=(a.sub.1, a.sub.2. . . a.sub.m) (6)
More specifically, the Fuzzy backward reasoning device 5 receives the feature quantities b: b.sub.1 to b.sub.n from the outside, and reads out the causality relation: r.sup.1 to r.sup.n from the causality relation storage device 3. It further estimates a.sub.1 to a.sub.m with use of the batch reasoning device 51 and outputs those reasoned values.
Referring now to FIG. 8, a flow chart indicative of operation of the prior art Fuzzy backward reasoning device 5 is illustrated. The operation will be described illustratively. It is assumed that the causality relation R and the feature quantity b are inputted into the batch reasoning device 51 from the outside, as follows for example. ##EQU3##
First in step S1, the number p of solutions is initialized. Then, in step S2, a matrix U is calculated according to the following equation. ##EQU4## Here, (b.sub.j, 1.0) indicates a closed interval from b.sub.j to 1.0. .phi. means no solution. Likewise, in step S3, a matrix is calculated according to the following relation. ##EQU5## In the example expressed by the equations (7), (8), , are given as follows. ##EQU6##
In step S4, the number L of combinations of non-.phi. elements of respective columns of U is calculated. In case of U of (11). EQU L=3.times.3.times.1=9 (13)
In step S5, if the number L is zero, then there is no solution, and the reasoning operation advances to step S12 to output "no solution". If the number L is not zero, then a possibility of L solutions being existent must be taken into consideration. In step S6, one element of each column of which is not .phi. is taken out, and remaining elements are taken out from to form a matrix .phi..sup.k. In the present example W includes 9 combinations, one of which is for example as follows. ##EQU7##
In step S7, the intersection of the ith row of .sup.k are taken out to yield the ith element of . W of the expression (14) gives EQU a=[(0.9, 1.0) 0.0 0.0] (15)
In step S8, if there is any .phi. element among those elements in , i.e., if there is yielded any intersection in some row of W.sup.k, then in this case is not taken as a reasoning result. In step S9, the number of reasoned results is counted. In step S10, a resulting reasoned result, for example of the expression (15) is outputted. Finally, after L combinations of W are estimated, in step S11 a decision is done that if P=0 or there is no reasoned result yielded finally, then the operation jumps to step S12 to output "no solution".
The prior art Fuzzy backward reasoning device arranged as described above however has problems as follows. The reasoning can be initiated only after the entire feature quantities b.sub.1 to b.sub.n have been observed, thus requiring much time for the reasoning. Additionally, a processor having a higher computational capability is required because the associated computation must be done at a spot.
On the other hand, there is known a prior art target recognition device disclosed, for example as a typical, in Bir Bhanu: Automatic Target Recognition: State of the Art Survey, IEEE Transactions on Aerospace and Electronics, Vol. AE5-22, No. 4, PP 364-379 (1986), as illustrated in FIG. 9. As illustrated in the figures, designated at 101 is a target to be recognized, 151 is an image sensor for observing the target 101 and outputting image information, 152 is a preprocessor for receiving the image information from the image sensor 151, 153 is a target director for receiving an output from the preprocessor, 154 is a segmentation for receiving an output from the target detector 153, 155 is a recognizer for receiving an output from the segmentation 154, 156 is a prior typical target recognition device composed of the image sensor 151, preprocessor 152, target detector 153, segmentation 154, and recognizer 155, and 7 is a behavior deciding device for receiving an output from the target recognition device 156.
The target recognition device 156 shown in FIG. 9 is to recognize the target 101 as an image, and is operable as follows. First, the image sensor 151 observes the target 101 as an image. For the image sensor 151, there are sometimes useable an infrared sensor and a millimeter wave radar. The preprocessor 152 is to receive and previously process an image, the output from the image sensor 151, and output a processed result. In the preprocessing, there are performed restriction of any noise and clutter and emphasis of the contour of the image. The target detector 153 is to receive the image data processed previously as such, and detect from the data a region where there is existent one which might be considered to be a target and output it. The segmentation 154 performs image processing with high accuracy for the detected region, and extracts and outputs a target from the background highly accurately. The recognizer 155 collates the target image to extracted with images involved in a data base and outputs the name of the kind of a so-coincident target. This is an output from the prior typical target recognition device 156. The output is fed to the behavior deciding device 7 as a guide to decide a behavior for responding to the target.
Such prior art target recognition devices recognize a target based upon a single kind of information (image information, for example, if an image sensor is used.) available from a sensor with use of a Neuman type computer as described above. The devices however suffer from not obtaining any information concerning a target if there is outputted no image information from the image sensor 151 because a target is located at a long distance and hence to difficult to be observed as having any shape or a target is in clouds and/or in smoke. Furthermore, the device has a problem that it is unclear to what degree information for recognition of a target from the sensor is reliable.